Incest has been shown to produce offspring that are not fully developed. This is due to the fact that the DNA genes cannot fully form because of the overlap from the parents being related. It is not that bad in the first generation but if it keeps going it will get worse. This is one of the problems with the old monarchs that kept inbreeding to keep the crown in the family.
Incest in itself has been proven to create unhealthy offspring. A related set of family members should strive to find others that are not living under their homes. Incest can and has lead to actions of domestic sexual abuse towards children and adults alike. If incest is shown as ok, adult or not, it will lead to loopholes of the law like molestation of children or young adults.
Most sexual encounters do not result in a birth. Many people who have relationships or marry never have genetic children together; some people in consanguinamorous relationships choose not to. So, we must recognize the differences between sex, marriage, parenting, and reproduction, and not ban the first three because of concerns about the last one.
But let's deal with that last one. Most births to consanguineous parents do not produce children with significant birth defects or other genetic problems; while births to other parents do sometimes have birth defects. There are happy, healthy, bright, attractive people born to close relatives who are productive members of society. We all know some, whether we know it or not, and whether they know it or not. It is that common. We don’t prevent other people from marrying or deny them their reproductive rights based on increased odds of passing along a genetic problem or inherited disease. For example, it is entirely legal in the US and most other places for someone with Huntington's Disease to date, have sex, marry, and have genetic children. How can such rights be denied to people who are genetically healthy, simply because they are close relatives?
There are US states and there are countries where consanguinamory is not illegal or at least it isn't prosecuted. Sweden will legally marry half-siblings in some circumstances. A comparison of the rate of genetic problems in these places to places that criminalize and actively prosecute consanguinamory reveals no discernible increase in genetic problems in the places that embrace this relationship right.
If a natural talent or gift runs in the family, the children born to consanguineous parents will be more likely to inherit and manifest that beneficial result as well; a birth benefit. But there are increased odds of problem with births to older parents, too. There's no stigma assigned to that, and it isn't illegal for older people to date, have sex, marry, and have genetic children together.